EIN 6936 Nonlinear & Dynamic Optimization

Objective: Get exposed to the theory of nonlinear and discrete dynamic programming and build foundations for their applications.

References:
Nonlinear Programming: Theory and Algorithms, M. S. Bazaraa, et al., 2006.
Convex Optimization, S. Boyd, L. Vandenberghe, 2004.
Convex Analysis, R. T. Rockafellar, 1996.
Dynamic Programming: Models and Applications, E. V. Denardo, 2003.

Topics:

• I. Deterministic dynamic optimization
•    Sequential decision making
•    Principle of backward recursion; optimality principle
•    Optimal paths in finite acyclic directed networks; myopic policies
•    Asset replacement models
•    Multi-stage production/inventory planning models
•    Resource allocation models
•    Finite horizon investment models
• II. Stochastic dynamic optimization
•    Probabilistic state transitions and recursive equations
•    Gambling models; game of chance models
•    Multi-stage newsboy models
•    Stock-option models
•    Modular functions and monotone policies
• III. Elements of basic topology
•    Metric spaces
•    Open and closed sets
•    Compact sets
•    Continuous functions; Weierstrass' theorem
• IV. Convex analysis
•    Convex sets
•    Convex hulls
•    Convex functions
•    Convex optimization problems
• V. Unconstrained nonlinear optimization
•    Descent methods
•    Gradient descent method
•    Newton's method
•    First/second order necessary conditions
•    One-dimensional search algorithms
•    Unimodal functions
• VI. Constrained nonlinear optimization
•    Linear equality constraints
•    Newton's method with equality constraints
•    Inequality constraints
•    KKT conditions
•    Penalty functions
•    Interior-point methods
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